An efficient alternative approach for the solution of an interval integer transportation problem
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Abstract The purpose of an Original Possible Solution (IFS) of an integer transportation interval problematic constructions an essential part of finding a minimum total transportation interval cost solution. Better initial feasible interval solution will result in fewer iterations achieving the minimum total cost solution for the interval. Various methods are obtainable in the fiction to achieve a better original possible result to the problem of interval transport. A new, effective method with row penalties is proposed in this paper to find an initial feasible interval solution to an interval transport problem. One numerical illustration demonstrates the new process. Thus, our new approach can be regarded as an alternate technique for achieving an original possible interval solution to a problem of integral interval transport.Keywords:
Interval arithmetic
Transportation theory
Based on the standard expression of interval number and the rules of four algebraic operation of standard interval number,the application of standard interval function was introduced.The standard interval function can deal with some problems that Grey number or interval analysis can't.The solution to standard interval linear equations was researched and the method was used in mechanical error analysis.An example was given,the results of several error analysis method were compared,it is shown that the standard interval function is more effective than interval analysis.
Interval arithmetic
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Abstract Interval arithmetic is the mathematical structure, which for real intervals defines operations analogous to ordinary arithmetic ones. This field of mathematics is also called interval analysis or interval calculations. The given math model is convenient for investigating various applied objects: the quantities, the approximate values of which are known; the quantities obtained during calculations, the values of which are not exact because of rounding errors; random quantities. As a whole, the idea of interval calculations is the use of intervals as basic data objects. In this paper, we considered the definition of interval mathematics, investigated its properties, proved a theorem, and showed the efficiency of the new interval arithmetic. Besides, we briefly reviewed the works devoted to interval analysis and observed basic tendencies of development of integral analysis and interval calculations.
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The paper presents an unambiguous modelling of imprecisely defined shapes of closed curves using classical and directed interval arithmetic. The authors focus on the development of an effective strategy of modelling interval smooth closed curves (which enforce $$C^2$$ continuity in points at which adjacent interval segments join) using interval cubic Bézier segments. For this purpose, algebraic relationships between Bézier and de Boor control points, formerly known for precisely defined curves, are generalized. We obtain interval control points that define interval closed curves. Additionally, the reliability of such way of modelling of closed curves is examined. We directly apply classical and directed interval arithmetic to mentioned relationships and try to solve obtained interval systems of algebraic equations. However, we obtain ambiguous solutions. Therefore, we propose our new strategy of modification of directed interval arithmetic to obtain reliable and unambiguous shapes of interval closed curves.
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Uncertainties widely exist in structural engineering.Interval analysis is the most effective method to calculate uncertain structure.However,interval analysis could not be applied widely in practical engineering because of low precision.Particle swarm optimization(PSO) is proposed to deal with interval analysis of uncertain structure in this paper to replace interval arithmetic by global optimization.It is shown that PSO has the more precise results than other interval arithmetic.
Interval arithmetic
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Interval arithmetic
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This work presents a probabilistic interval analysis method for the tolerance analysis of discrete and continuous apertures. Given the knowledge of the interval tolerances, and starting from inclusive pattern bounds obtained using state-of-art interval analysis tools, a novel methodology is here introduced that allows to compute, in closed-form, the probability distribution of the random pattern occurrences within the interval bounds. A numerical example is reported showing the advantage of the proposed approach with respect to the state-of-art interval analysis methods.
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Tolerance Analysis
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Analytic performance models are often used for predicting the performance of computing systems. Existing models accept single valued parameters as input and produce single valued performance measures as outputs. This research proposes to associate intervals or ranges of values with performance measures and key system parameters. Such an approach is appropriate when exact parameter values are unknown but approximate ranges for parameters may be estimated. Conventional arithmetic cannot handle intervals and interval arithmetic-based techniques are required. The paper reports on the feasibility of application of interval arithmetic in the solution of existing well-known models of computing systems. One of the problems with using interval arithmetic is the potential loosening in the interval for the model output: the computed interval may be wider than the actual interval. A computational method based on the notion of interval splitting is introduced in this paper for controlling this problem. The technique is found to be effective in the context of a number of models.< >
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